Dan SchwartzHow many numbers are there? If your answer is “an infinite number,” then you have unwittingly adopted a Platonic approach to mathematics.
Such is Dr. Harry Binswanger’s claim in his OCON 2024 talk “Saving Math from Plato’s Progeny.” The progeny discussed include such figures as Bertrand Russell and Georg Cantor. You may have heard of Cantor’s view that the infinity of numbers is greater than the infinity of even numbers alone. Dr. Binswanger explains why this too is a relic of Platonism.
Dr. Binswanger challenges premises familiar to most of us from high school mathematics. If you think we need irrational numbers to measure the hypotenuse in certain right triangles, for example, you will learn why that is not the case.
This talk is part of Dr. Binswanger’s continued work in developing an Aristotelian, perception-based approach to mathematics. It builds on his OCON 2023 talk “Saving Math from Plato.”
During the Q&A, Dr. Binswanger addresses questions on a variety of topics, such as:
- How to understand limits;
- The meaning of negative numbers;
- Whether there is a shortest possible length.
Brandon Lisi
